Ankle rehabilitation robots are widely used due to nerve injuries and sports injuries leading to decreased mobility of the ankle joint. However, the motion of most ankle rehabilitation robots has distinctions with human ankle physiological structure. In order to achieve more accurate rehabilitation training of the ankle joint, this paper proposes a novel 3-UPU parallel rehabilitation mechanism. In a certain range, the mechanism can perform rotation around any axis within the midplane, which means that the mechanism can achieve non-fixed-point rotation around the instantaneous axis of the ankle joint. The mechanism has three degrees of freedom and can perform ankle pronation/supination and inversion/eversion movements. Taking into account the structural differences of different human bodies, the rotating axis of the mechanism can be adjusted in both height and angle. Then, the workspace of the mechanism was solved, and the size parameters of the mechanism are analyzed based on the characteristics of the size parameters of the mechanism and the motion range of the ankle. A genetic algorithm was employed to optimize the mechanism’s parameters. Next, the motion trajectory of the mechanism was planned, and the length change of the mechanism driving pair during the motion planning of the angle was obtained through kinematics simulation. Finally, experimental verification of the above rehabilitation training methods indicates that the mechanism meets the requirements of ankle rehabilitation.